Terahertz band of the electromagnetic spectrum is the region whose frequency lies between 0.3 THz and 10 THz. This region located between the microwave and optical part of the spectrum. This is one of the most wonderful and also the most complicated band of the spectrum. In the past few years numerous applications of this band have been proposed by researchers. Nowadays, THz technology has many applications in medicine, astronomy, archaeology, high speed communication and security. The most important challenges in THz technology are sources and detectors. Many researches have been done by scientists in last two decades to overcome these challenges. One of the most efficient detector is the one which is based on electro-optic sampling principle. In this dissertation we have studied and simulated the THz detectors which are based on nonlinear crystals. In the beginning, we reviewed the THz technology in brief. After that we studied the nonlinear materials and their behaviour. Then we introduce our simulation algoritm and we successfully simulated two important nonlinear phenomenas which are the fundamentals of THz sources and detectors and we verified our simulation and its results. In the end, we studied the dispersion in the nonlinear ZnTe crystal and simulated its effect on detection of THz pulses. Keywords : Nonlinear crystal, THz detector, Electro-optic sampling, FDTD, Dispersion